Performance simulation of the perovskite solar cells with Ti3C2 MXene in the SnO2 electron transport layer

MXenes, a class of two-dimensional (2D) transition metal carbides and nitrides, have a wide range of potential applications due to their unique electronic, optical, plasmonic, and other properties. SnO2–Ti3C2 MXene with different contents of Ti3C2 (0.5, 1.0, 2.0, 2.5 wt‰), experimentally, has been used as electron transport layers (ETLs) in Perovskite Solar Cells (PSCs). The SCAPS-1D simulation software could simulate a perovskite solar cell comprised of CH3NH3PbI3 absorber and SnO2 (or SnO2–Ti3C2) ETL. The simulation results like Power Conversion Efficiency (PCE), Open circuit voltage (VOC), Short circuit current density (JSC), Fill Factor (FF), and External Quantum Efficiency (EQE) have been compared within samples with different weight percentages of Ti3C2 MXene incorporated in ETL. Reportedly, the ETL of SnO2 with Ti3C2 (1.0 wt‰) effectively increases PCE from 17.32 to 18.32%. We simulate the role of MXene in changing the ideality factor (nid), photocurrent (JPh), built-in potential (Vbi), and recombination resistance (Rrec). The study of interface recombination currents and electric field shows that cells with 1.0 wt‰ of MXene in SnO2 ETL have higher values of ideality factor, built-in potential, and recombination resistance. The correlation between these values and cell performance allows one to conclude the best cell performance for the sample with 1.0 wt‰ of MXene in SnO2 ETL. With an optimization procedure for this cell, an efficiency of 27.81% is reachable.


Methodology and simulations
SCAPS-1D is a software used for one-dimensional simulations.It calculates energy bands, current-voltage characteristics, and external quantum efficiency by solving continuity equations for electrons and holes and the Poisson equation 45 .The software can also calculate recombination profiles and electric field distribution for layers and interlayers.The basic continuity equations used by this software for electrons and holes are: where µ n and µ p are the electron and hole mobility respectively, D n (D n ) is the electron (hole) diffusion coefficient, E is the electric field, q is the electron charge, and p(n) is the hole (electron) density.The recombination rate of electrons and holes (U n,p ) can be calculated through the equations mentioned above: where G is the electron-hole generation rate.
In a recent experiment, researchers incorporated Ti 3 C 2 MXene in SnO 2 ETL to enhance the efficiency of PSCs.To understand how this enhancement is achieved, simulations were conducted on two types of PSCs.The first one had the architecture of ITO/SnO 2 /CH 3 NH 3 PbI 3 /Spiro-OMeTAD/Ag, while the second one had the architecture (1) of ITO/SnO 2 -Ti 3 C 2 (0.5, 1.0, 2.0 and 2.5 wt.‰)/CH 3 NH 3 PbI 3 /Spiro-OMeTAD/Ag (Fig. 1).The simulation work used data provided by the original experimental work 44 .
The material parameters for the pristine sample are selected from published experimental data and listed in Table 1.Interfacial parameters for simulation are shown in Table 2.In this table, N A and N D denote acceptor and donor densities, ε is relative permittivity, χ is electron affinity, E g is band gap energy, and N t is defect density.N C and N V are the effective densities of conduction and valance band states, respectively.To estimate the thickness of the layers, the SEM image provided in the experimental work 34 was used.In addition, the electron/hole thermal velocity for each layer was set to 10 7 cm/s, simulated light conditions were AM1.5G, and the simulation temperature was 300 K.According to a study 28 , incorporating Ti 3 C 2 MXene into the layers of PSC does not affect the band gap energy.However, it does reduce the WF in the layers, which changes the electron affinity of the layers 28 .This means that the band gap energy will remain the same for MXene-added structures.Moreover,   34 , b Ref. 46 , c Ref. 47 , d Ref. 48, e Ref. 49 , f Ref. 50 , i Ref. 51,52 .
From spectrum i the electron affinity of the MXene-added ETL has been measured to be 4.63 eV 34 .It has been reported that the efficiency enhancement of PSCs is mainly due to the increased mobility of the layers when MXene is added.In this work, we have adopted an electron mobility of 1.23 × 10 -5 cm 2 /V s for the MXene-assisted ETL 34 .This value shows an order of magnitude increase compared to the bare SnO 2 ETL.In the simulations, all parameters except for the MXene concentration in the ETL of the cells are kept constant.The values of carrier capture cross-section layers in PSCs with SnO 2 ETL and MXene-added ETL are considered to be 1 × 10 -15 cm 2 .

Results and discussion
The Fig. 2 illustrates the agreement between the experimental current density-Voltage (J-V) data for PSCs with SnO 2 and SnO 2 -MXene (1.0 wt‰) ETLs and simulation results.In the same figure, the theoretical External Quantum Efficiency (EQE) curve closely matches the measured one.This indicates that the model was able to successfully explain the process of photovoltaics.It's worth noting that the simulated photovoltaic parameters closely follow the measured values, as shown in the graph's inset.The original paper 34 does not provide EQE data for the PSCs of SnO 2 -MXene at varying concentrations (0.5, 1.5, 2.0, and 2.5 wt‰).We present simulated J-V curves for the samples, which closely match the experimental ones shown in Fig. 3.In this figure, the calculated photovoltaic characteristics obtained from the fitting are being compared with the measured ones, where a high degree of concurrency can be seen between them.The generated EQE curves are shown in the insets.
For determining integrated current density, we combine the photon flow at a certain wavelength, leading to the flow of electrons leaving the solar cell at this wavelength 53 .We have, where ph, is the photon flux of AM1.5.The simulated and experimental EQE spectra and their corresponding integrated currents density are depicted in Fig. 4. The calculated integrated current density for the SnO 2 -based cell is 19.93 mA cm -2 .When 1.0 wt‰ MXene is added to the device, it increases to 20.29 mA cm -2 .The deviation between the integrated current from EQE and the values obtained from the simulation of J SC values (presented in    34 .R s is in series with other components and results in a shift in the Nyquist spectrum along the real axis away from the origin.The term R rec denotes the phe- nomenon of electron capture, where an electron or hole moves from the conduction or valence band to a defect in the bandgap or to surface states 54,55 .Capacitance in IS corresponds to the storage of electrical energy.Physically, capacitance arises either due material polarisation (geometric capacitance), or due to local inhomogeneity in the distribution of free charge (electrochemical capacitance), usually related to charge dynamics.R rec is inversely proportional to charge recombination.Higher R rec suggests lower carrier recombination (better hole-blocking ability) 34 .In Fig. 6, Nyquist plots are drawn for voltages of 0 V, 0.4 V and V OC .Among the PSCs of ETL with MXene, the resistance value of R rec is ordered as SnO 2 -Ti 3 C 2 (1.0 wt‰) > SnO 2 -Ti 3 C 2 (0.5 wt‰) > SnO 2 -Ti 3 C 2 (2.0 wt‰) > SnO 2 -Ti 3 C 2 (2.5 wt‰), where a higher resistance is better for electron collection.This implies that the least charge recombination occurs at the interface, resulting in the highest FF of SnO 2 -Ti 3 C 2 (1.0 wt‰).This    It is evident that the V OC increases with the intensity of illumination; however, it almost reaches saturation at high light intensity.We used 56,57 to calculate the n id s.
where k is Boltzmann's constant, T is temperature, q is the elementary charge, kT q is the thermal voltage and is equal to 0.026V at room temperature, and I 0 is reference intensity at one Sun.
Figure 7b displays the curves of V OC changes against Ln(I/I 0 ) and the slopes obtained for calculating the n id values.The bulk and interfacial Shockley-Read-Hall (SRH) recombination are formulated according to Refs. 58,59.
where n i is the equilibrium charge density, σ n,p is the electron and hole absorption cross-section, and n(p) is electron (hole) density under the non-equivalence condition.E i and E t represent the intrinsic and trap defect energy levels, respectively, υ th represents the thermal velocity and τ n,p is the carrier lifetime.In Fig. 8, we can see the bulk and interfacial recombination currents, as well as cap V OC s , and calculated n id s .It's worth noting that band-to-band recombination was found to be negligible.In the PSC with bare ETL of MXene, the ideality factor is relatively close to 2 (n id = 1.60).
When additive MXenes are introduced into the ETL of solar cells, the ideality factor values become closer to 1.This indicates that the interfacial mechanism, rather than bulk recombination, dominates in the MXeneassisted ETL cells.Among these cells, the one with 1.0 wt‰ of MXene shows the highest ideality factor and V OC values.This suggests that adding 1.0 wt‰ of MXene into the SnO 2 ETL makes the interface recombination least effective, resulting in the best cell performance.
It is well established that incorporating MXenes in the structure of PSCs can enhance their performance.However, it is important to note that increasing the weight percentage of MXene in the SnO 2 ETL beyond 1.0 wt‰ may lead to a reduction in the V OC , which requires further discussion.This same observation also applies to cells with 0.5 wt‰ of MXene.To remove ambiguities, we plotted the carrier lifetime of the absorber layer against the weight percentage of MXene in ETL (Fig. 9).It can be observed that the carrier lifetime reaches its peak when 1.0 wt‰ MXene is present in the SnO 2 ETL structure.This indicates that the charge carriers generated in this cell will have a longer effective time for extraction by the charge transport layers, in comparison to the other cells.In Fig. 10, the electric field distribution of cells at the ETL/absorber interface was studied for applied voltages that were less than, equal to, and greater than the V OC .It was observed that the 1.0 wt‰ MXene-added cell had a stronger electric dipole formed at the ETL/absorber interface, which could establish a significant potential difference across the ETL.This would lead to a shorter extraction time for the electrons from the ETL, as compared to the charge carrier lifetime in the absorber layer 34,60,61 .As a result, the photogenerated charge carriers in the absorber layer could be extracted immediately.On the other hand, due to the weaker dipole ( 6) moment of the other cells formed at the ETL/absorber, the photogenerated carriers took much more time to be collected.It has been observed that the addition of MXene to SnO 2 ETL cells results in higher recombination, which significantly reduces their overall performance.However, it has been found that the MXene-assisted cells with 1.0 wt‰ MXene-added-SnO 2 ETL show better performance compared to other such cells.This is due to the fact that interfacial recombination plays a more crucial role than bulk recombination in determining cell performance, as indicated by the higher ideality factor of these cells.In cells containing MXene, there is a  correlation between n id s and cell performance.This correlation can be explained through the inset in Fig. 9, where the curves of V OC and n id versus the MXene weight percentage follow the same pattern as the carrier lifetime in the absorber layer.Therefore, in these cells, a lower n id indicates a higher interfacial recombination current, resulting in a less efficient cell.
In literature, the correlation between quasi-Fermi level splitting (QFLS) and charge carrier densities (n and p) in the absorber layer has been discussed (62).
where β is a parameter defining the relationship between the carrier density and the perturbation of the QFLs from equilibrium and is equal to 1 or 2, and n i is the equilibrium charge density.In brief, if the charge carrier densities undergo the condition n ≈ p , the bulk recombination will dominate.Meanwhile, the presence of a dominant charge carrier, e.g., n >> p (or p >> n ), makes the interfacial recombination the dominant mechanism.Figure 11 shows n and p for cells with and without MXene, and Table 3 provides values of these values at the middle of the absorber layer.In the cell with bare SnO 2 ETL shows better n ≈ p is condition compared to the other cells.This indicated that bulk recombination dominates and n id is likely to be close to 2. On the other hand, in MXene-assisted cells, the condition n >> p is satisfied, and the n id is relatively close to 1.Among these cells, the one with 1.0 wt‰ of MXene has the lowest p/n ratio, which confirms the highest n id .
After gaining more insights into the role of incorporated MXenes into the SnO 2 ETL, we assessed the photocurrent density using Eq. ( 10), where J(V ) and J dark are the current density under light and the dark current density, respectively 62,63 .
The electric field established in the absorber layer is E = V bi −V d , where V bi is the built-in potential, and d is the thickness 61 .The drift caused by such an internal electric field makes a photogenerated current.This photogenerated current J ph (V ) is formulated as 64,65 , where µ is charge carrier mobility, τ is charge carrier lifetime, V is the applied voltage, and d is the sample thickness.The equation above provides a practical method to determine the built-in potential by finding the intersection of the J ph (V ) curve with the voltage axis.
Figure 12 illustrates the J ph (V ) of the cells with and without MXene in their ETL structure.This figure clarifies how to derive the V bi .for each sample.Improving the V OC is crucial in photovoltaic structures as it effectively reduces interfacial recombination.On the other hand, the voltage limit of the V OC is determined by the V bi which is vital for achieving better cell performance [66][67][68][69][70] .As depicted in the figure, the sample containing 1.0 wt.‰ MXene in the ETL displays the highest V bi , which is why it has the highest PCE among all samples.
In the last part of this work, an optimization procedure of the SnO 2 -Ti 3 C 2 (1.0 wt‰) is presented, and it is hoped that the results of this optimization will have a significant impact on practical features of photovoltaic science, as well as understanding the role of the thickness of the layers.
Figure 13 shows a contour plot that displays the variation of the thickness of the SnO 2 -Ti 3 C 2 (1.0 wt‰) ETL and the absorber layer, ranging from 10 to 40 nm and 400 nm to 1200 nm, respectively.The optimal thickness for the absorber layer is 700 nm, while the optimal thickness for the ETL is 10 nm.We will use these values for the ETL and absorber thickness parameters throughout the optimization process.
Figure 14 illustrates the relationship between the thickness of the HTL and the absorber.The range of HTL layer thickness considered in this study is between 100 and 700 nm.After optimization, a thickness of 700 nm was selected as the most suitable for the HTL layer thickness.

Conclusion
A numerical analysis was conducted on devices with and without 2D MXene in their SnO 2 ETLs using SCAPS-1D software.The study found that a device architecture of ITO/ETL/CH 3 NH 3 PbI 3 /Spiro-OMeTAD/Ag with SnO 2 -Ti 3 C 2 (1.0 wt‰) as the ETL achieved a relatively high PCE of 27.81%.It is believed that the added MXene plays a crucial role in reducing the interfacial recombination, which is the primary reason for the improved performance of the cell.By calculating the ideality factor (n id ), we established a correlation between this quantity and the cell performance.We found that the sample with the highest efficiency also had the highest n id value of 1.53.The improvement in efficiency in PSCs can be credited to the increase in R rec , a parameter that explains the enhancement in efficiency.This parameter demonstrates that IS is an easy and alternative technique for obtaining information about PSCs.

Fig. 2 )
Fig. 2) is around 10%.This indicates good accuracy of our J-V measured values.The integrated current density of SnO 2 -Ti 3 C 2 (0.5 wt‰), SnO 2 -Ti 3 C 2 (2.0 wt‰), and SnO 2 -Ti 3 C 2 (2.5 wt‰) are 20.13 mA cm -2 , 20.41 mA cm -2 , and 20.58 mA cm −2 , respectively.Figure 5 shows the result of the simulation of EQE and integrated current density for SnO 2 -Ti 3 C 2 (0.5 wt‰), SnO 2 -Ti 3 C 2 (2.0 wt‰), and SnO 2 -Ti 3 C 2 (2.5 wt‰).It can be seen that the amount integrated current density follows the order of MXene weight percentage in the SnO 2 ETL.The Nyquist plots of solar cells of different ETLs with recorded IS spectra are shown in Fig. 6.The R rec s calcu- lated from fitting the semicircle Nyquist plots are shown in the same Fig.The semicircle is observed for all conditions, and it starts at a high frequency and ends at a low frequency.This semicircle can be fitted to an equivalent circuit.The wires and ITO substrate are largely associated with R s .The main observed semicircle represents R rec , and the interfacial capacitance (C) at the ETL/perovskite interface34 .R s is in series with other components and results in a shift in the Nyquist spectrum along the real axis away from the origin.The term R rec denotes the phe- nomenon of electron capture, where an electron or hole moves from the conduction or valence band to a defect in the bandgap or to surface states54,55 .Capacitance in IS corresponds to the storage of electrical energy.Physically, capacitance arises either due material polarisation (geometric capacitance), or due to local inhomogeneity in the distribution of free charge (electrochemical capacitance), usually related to charge dynamics.R rec is inversely proportional to charge recombination.Higher R rec suggests lower carrier recombination (better hole-blocking ability)34 .In Fig.6, Nyquist plots are drawn for voltages of 0 V, 0.4 V and V OC .Among the PSCs of ETL with MXene, the resistance value of R rec is ordered as SnO 2 -Ti 3 C 2 (1.0 wt‰) > SnO 2 -Ti 3 C 2 (0.5 wt‰) > SnO 2 -Ti 3 C 2 (2.0 wt‰) > SnO 2 -Ti 3 C 2 (2.5 wt‰), where a higher resistance is better for electron collection.This implies that the least charge recombination occurs at the interface, resulting in the highest FF of SnO 2 -Ti 3 C 2 (1.0 wt‰).This

Figure 7 .
Figure 7. Plots of V OC versus.(a) (I/I 0 ), (b) the calculated slope of the V OC versus ln (I/I 0 ) curves for PSCs with SnO 2 and MXene-assisted ETLs are shown.

Figure 10 .
Figure 10.The Absolute electric field at the ETL/Absorber interface for V < V OC (a), V ≈ V OC (b), and V > V OC (c).

Figure 13 .
Figure 13.The effect of the SnO 2 -Ti 3 C 2 (1.0 wt‰) ETL and absorber thickness variation on the cell performance.

Figure 14 .
Figure 14.The effect of the HTL and absorber thickness variation on the cell performance.
a Ref.

Table 2 .
Interfacial parameters used in the simulation by SCAPS for ITO/SnO 2 /CH 3 NH 3 PbI 3 /Spiro-OMeTAD/Ag PSCs structures.Above the highest E V Above the highest E V Above the highest E V